Resonance phenomena simulated by finite differences and biased noise inputs

In Lecture-21.nb, a second-order differencing scheme that iteratively solved  y'' + βy' + γy=0  with the specification of two initial values.
Modify this to add a little random noise to y[i] at each step and observe how this behaves---this version will store the noise added at each iteration so that it can be visualized later....

"index_1.gif"

Setting up a function that takes particular parameters and a "noise amplitude" of "index_2.gif"

"index_3.gif"

"index_4.gif"

"index_5.gif"

"index_6.gif"

"index_7.gif"

"index_8.gif"

"index_9.gif"

"index_10.gif"

Now suppose there is a periodic bias that tends to kick the displacement one direction more than the other:

"index_11.gif"

"index_12.gif"

Generate the data set---this takes quite a while

"index_13.gif"

"index_14.gif"

"index_15.gif"

"index_16.gif"

Spikey Created with Wolfram Mathematica 6